What is the integral from 0 to infinity of x*e^{-x} ?

The integral from 0 to infinity of x*e^{-x} is 1

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integral from 0 to infinity of x*e^{-x}

\int_{0}^{\infty} x \cdot e^{- x} d x

1

Solution steps

\int_{0}^{\infty} x e^{- x} d x

Compute the indefinite integral:

\int x e^{- x} d x = - e^{- x} x - e^{- x} + C

Compute the boundaries:

\int_{0}^{\infty} x e^{- x} d x = 0 - (- 1)

= 0 - (- 1)

Simplify

= 1

\frac{1}{2 x + 1}, at a = 3

\frac{d y}{d x} = \frac{9}{x}

\frac{x ^{2} - 3 x + 2}{2 x + 1}

\frac{e ^{- 2 s}}{s ^{2} - 2 s + 5}

\frac{\partial}{\partial x} ((7 x + 3 y)^{5})

What is the integral from 0 to infinity of x*e^{-x} ?
The integral from 0 to infinity of x*e^{-x} is 1